ANTISYMMETRIC

Etymology

Adjective

antisymmetric (not comparable)

(set theory, order theory, of a binary relation R on a set S) Having the property that, for any two distinct elements of S, at least one is not related to the other via R; equivalently, having the property that, for any x, yS, if both xRy and yRx then x=y.

   x R y \(\Leftrightarrow\) 'x divides y' for all x, y ∈ N.

(linear algebra, of certain mathematical objects) Whose sign changes on the application of a matrix transpose or some generalisation thereof

(of a matrix) Whose transpose equals its negative (i.e, MT = −M);

(of a tensor) That changes sign when any two indices are interchanged (e.g, Tijk = -Tjik);

    \(\textstyle T_S\equiv\frac{1}{2}(T+T^T)\),     \(\textstyle T_A\equiv\frac{1}{2}(T-T^T),\)     (3.47)

(of a bilinear form) For which B(w,v) = -B(v,w).

Synonyms

• (linear algebra): skew-symmetric

Source: Wiktionary



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Word of the Day

25 October 2024

SUPERIORITY

(noun) displaying a sense of being better than others; “he hated the white man’s superiority and condescension”


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Coffee Trivia

According to Guinness World Records, on 25 September 2016, the Birla Institute of Management Technology (India) in Uttar Pradesh, India, constructed the largest coffee cups pyramid consisting of 23,821 cups. They used paper takeaway coffee cups to build the pyramid.

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